- #1

tanaygupta2000

- 208

- 14

- Homework Statement
- The concentration p(r,t) of ink diffusing in water is governed by the diffusion equation

∂p/∂t = D∇^2(p)

where D is a parameter known as diffusion constant. What is the average time taken for a molecule of ink to spread by a root mean square distance R?

(a) √(R/D)

(b) R/√D

(c) R^2 /D

(d) RD

- Relevant Equations
- ∂p/∂t = D∇^2(p)

I assumed p(r,t) as p(r,t) = R(r)T(t) as Separation of Variables method. I got the expression of T(t) as

T(t) = C

and got a non-linear differential equation in R(r) as

d

(I assumed r to be the radial distance in spherical coordinates)

Now I'm not getting how to solve this differential equation.

T(t) = C

_{1}e^{C2t}and got a non-linear differential equation in R(r) as

d

^{2}R/dr^{2}+ (2/r)dR/dr - (C/D)R = 0(I assumed r to be the radial distance in spherical coordinates)

Now I'm not getting how to solve this differential equation.